Network-Based Optimization Models

1. Network-Based Optimization Models Charles E. Noon, Ph.D. The University of Tennessee

2. Overview • What is a network? • Common network-based models for logistics • Shortest Path • Shortest Route • Service Area

3. Networks in a GIS • An interconnected set of lines representing possible paths from one location to another. • A network structure is defined by arcs (lines) and nodes (points). Their interaction is defined by topology. • Examples: • Road network • Shipping network • Railroad network • Air network

5. Basic Network-Based Optimization Models 1. Shortest Path 2. Single Vehicle Shortest Route (or Tour) 3. Service Area

6. Basic Prescriptive Modelsfor Transportation 1. Shortest Path (time or distance)

11. Basic Prescriptive Modelsfor Transportation 1. Shortest Path (time or distance) 2. Single Vehicle Shortest Route (or Tour) - aka Traveling Salesman Problem

14. Basic Prescriptive Modelsfor Transportation 1. Shortest Path (time or distance) 2. Single Vehicle Shortest Route (or Tour) - aka Traveling Salesman Problem 3. Service Area (time, distance or cost)

22. Session Overview • Prescriptive Analysis Continued 1. Shortest Path 2. Single Vehicle Shortest Route (or Tour) 3. Service Area • Optimization Models 4. Multi-Vehicle Routing 5. Transportation Problem 6. Facility Location • An Example

23. THE MODELING PROCESS Model Design Geographic Information Systems provide a platform to facilitate this process ... Data Collection and Analysis Build Model Validation Optimization Scenario Analysis Conclusion … and bring the power of visualization to Implementation

24. Optimization Models • Minimize or Maximize an Objective • total system cost (prodn costs, whse costs, trans cost, inv cost) • total profit • customer coverage • route time • Subject to Constraints • can be physical, financial, time • can be policy (inertia)

25. 4. Multi-Vehicle Routing • INPUTS: • road network • point layer of demand locations with amounts • point layer of depots with capacitated vehicles • time info if desired (windows, stop, load, travel) • OUTPUTS: • assignment of demand points to depots • assignment of demand points to vehicle • route schedule

30. 5. Transportation Problem • INPUTS: • road network • point layer of demand locations with amounts • point layer of supply locations with capacities • OUTPUTS: • transshipment flows from supply to demand

35. 6. Facility Location Models • INPUTS: • point layer of existing and candidate facility locations • fixed cost for “opening” a facility • point layer of client locations • cost (or profit) of service matrix • OUTPUTS: • set of facilities which should be opened • assignment of clients to facilities

41. An Example • A distributor to fast-food restaurants with 12 DC’s serving 3922 restaurants with 80 vehicles. • Currently, DC’s serve from 209 to 644 restaurants. • TransCad was first used to determine optimal weekly delivery routes under the current restaurant-to-DC assignments.

42. CURRENT STORE-TO-DC ASSIGNMENTS Total Mileage Per Week = 192,998

43. An Example • A distributor to fast-food restaurants with 12 DC’s serving 3922 restaurants with 80 vehicles. • Currently, DC’s serve from 209 to 644 restaurants. • TransCad was first used to determine optimal weekly delivery routes under the current restaurant-to-DC assignments. • TransCad was then used to re-assign restaurants-to-DC’s and determine approximately 400 vehicle routes that must be run each week.

44. OPTIMIZED STORE-TO-DC ASSIGNMENTS Total Mileage Per Week = 173,702

45. STORES WITH CHANGED ASSIGNMENTS Note: a total of 381 stores had changed DC assignments. Each dot may represent more than one store (in the same zipcode)

46. STORES WITH CHANGED ASSIGNMENTS Currently AssignedDC Optimally AssignedDC Cluster Net savings of 19,296 miles per week (10% reduction)